My prayers and wishes are with you, your grandmother and family members. Try dedicating some merit towards her for a favourable rebirth in this world or one of the heaven realms or purelands.
Namu Amida Butsu.

U can also ask nearest Lama to perform some rituals/prayers for your grandmother.
U can also ask people here in Prayers and Aspirations section to pray and practice for your grandmother. There are many practices that can be done in such situations, and many here practicing it occasionaly or even daily - my favourite is Chod practice (especialy longer one) which is very suitable in such cases.

This night my grandmother died.
My family is Catholic and they will do the usual rituals in which I will participate.

Is there additionaly something I can do that could benefit my grandmother?

Two years ago I was in Merigar during Shitro teachings, it was one of my first teachings, and I am quite the beginner which makes me not feel comfortable enough to do such a practise for her.

But maybe there are some other things that I can do that help here, where I can do nothing wrong? Some prayers?

http://monlam.org there are many prayers and rituals that you can dedicate for your grandmother. If you know how to do "sur" you can do that. Dewachen prayer or actually almost any prayer is also good.

/magnus

"We are all here to help each other go through this thing, whatever it is."
~Kurt Vonnegut

"The principal practice is Guruyoga. But we need to understand that any secondary practice combined with Guruyoga becomes a principal practice." ChNNR (Teachings on Thun and Ganapuja)

They said this terma of Buddhas epithet revealed by Nyala Pema Duddul is used by many lamas in Tibet these days to benefit the dead. It is liberation by hearing. The person who recite it need not have high realisation or good practices. This teaching is available in chinese language by the tulku who is one of the four main heart disciples of the late Lama Archuk in Yarchen Gar, this Rinpoche is himself the tulku of one of the main heart disciples of Nyala Pema Duddul. I attach a copy of the prayer and the you tube recitation by this Rinpoche

Get the materials (CD + booklet) on Shitro and do it, it is not so hard. Also you probably should have lung for Avalokiteshvara Khorwa Tongrtug, which also can be used to benefit dead people.
You can dedicate merit from your practice to her, do good deeds in her name or as others pointed out pay someone to do pujas.

Sorry to hear about your loss. I wish a lot of strength and compassion for you and your family to deal with this.

Child, if you are not hypocritical and out of control, that is conduct.
~ Padampa Sangye

You say such clever things to people, but you do not apply them to yourself.
The faults within you are the ones to be exposed.
~ Padampa Sangye

Get the materials (CD + booklet) on Shitro and do it, it is not so hard. Also you probably should have lung for Avalokiteshvara Khorwa Tongrtug, which also can be used to benefit dead people.
You can dedicate merit from your practice to her, do good deeds in her name or as others pointed out pay someone to do pujas.

Sorry to hear about your loss. I wish a lot of strength and compassion for you and your family to deal with this.

I also agree. Shitrö that ChNN teaches is very easy to perform, and usefull as all.

While tantric methods can be extremely powerful for those who know how to apply them, general advice for practices to benefit the dead emphasise Medicine Buddha practice, whichever you are familiar with, and the recitation of the King of Prayers (Samantabhadra bodhisattva's aspiration and conduct).